# CBSE 10th Math Sample Paper 2019 | Q17 Choice 2

#### Section C | Trigonometric Ratios & Identities

This 2019 CBSE class 10 Maths 3 mark question is from Trigonometry. Medium difficulty 3 mark question.

Question 17B: Prove that sin θ(1 + tan θ) + cos θ(1 + cot θ) = sec θ + cosec θ

## NCERT Solution to Class 10 Maths

### Explanatory Answer | CBSE Sample Paper Question 17 Choice 2

LHS: sin θ(1 + tan θ) + cos θ(1 + cot θ)
Substitute tan θ = $$frac{\text{sin θ}}{\text{cos θ}}$ and cot θ = $\frac{\text{cos θ}}{\text{sin θ}}$ = sin θ$1 + $$frac{\text{sin θ}}{\text{cos θ}}$ ) + cos θ$1 + $$frac{\text{cos θ}}{\text{sin θ}}$ ) = sin θ$ $$frac{\text{cos θ + sin θ}}{\text{cos θ}}$) + cos θ$$$frac{\text{sin θ + cos θ}}{\text{sin θ}}$ ) =$sin θ + cos θ) ($$frac{\text{sin θ}}{\text{cos θ}}$ + $\frac{\text{cos θ}}{\text{sin θ}}$) =$sin θ + cos θ) ($$frac{\text{sin^2 θ + cos^2 θ}}{\text{sin θ cos θ}}$)$We know sin2 θ + cos2 θ = 1)
= $\frac{\text{sin θ + cos θ}}{\text{sin θ cos θ}}$ = $\frac{\text{sin θ}}{\text{sin θ cos θ}}$ + $\frac{\text{cos θ}}{\text{sin θ cos θ}}$
= $\frac{1}{\text{cos θ}}$ + $\frac{1}{\text{sin θ}}$ = sec θ + cosec θ

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